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• W3048581314 abstract "We introduce the concept of analytical probabilistic modeling (APM) to calculate the mean and the standard deviation of intensity-modulated proton dose distributions under the influence of range uncertainties in closed form. For APM, range uncertainties are modeled with a multivariate Normal distribution p(z) over the radiological depths z. A pencil beam algorithm that parameterizes the proton depth dose d(z) with a weighted superposition of ten Gaussians is used. Hence, the integrals ∫ dz p(z) d(z) and ∫ dz p(z) d(z)2 required for the calculation of the expected value and standard deviation of the dose remain analytically tractable and can be efficiently evaluated. The means μk, widths δk, and weights ωk of the Gaussian components parameterizing the depth dose curves are found with least squares fits for all available proton ranges. We observe less than 0.3% average deviation of the Gaussian parameterizations from the original proton depth dose curves. Consequently, APM yields high accuracy estimates for the expected value and standard deviation of intensity-modulated proton dose distributions for two dimensional test cases. APM can accommodate arbitrary correlation models and account for the different nature of random and systematic errors in fractionated radiation therapy. Beneficial applications of APM in robust planning are feasible." @default.
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• W3048581314 date "2014-03-24" @default.
• W3048581314 modified "2023-09-26" @default.
• W3048581314 title "Analytical probabilistic proton dose calculation and range uncertainties" @default.
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• W3048581314 doi "https://doi.org/10.1088/1742-6596/489/1/012002" @default.
• W3048581314 hasPublicationYear "2014" @default.
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